Question

for #7 - 9, dilate the figure that is graphed according to the given scale factor (k). 7. k = 2 8. k =.5 9. k=-1/2

Explanation:

Step1: Recall dilation formula

For a point $(x,y)$ dilated about the origin with scale - factor $k$, the new point $(x',y')$ is given by $(x',y')=(k x,k y)$.

Step2: Dilate each vertex of the triangle for $k = 2$

Let's assume the vertices of the triangle $\triangle ABC$ have coordinates $A(x_1,y_1)$, $B(x_2,y_2)$, $C(x_3,y_3)$. The new vertices $A'(x_1',y_1')$, $B'(x_2',y_2')$, $C'(x_3',y_3')$ will be $A'(2x_1,2y_1)$, $B'(2x_2,2y_2)$, $C'(2x_3,2y_3)$.

Step3: Dilate each vertex of the triangle for $k = 0.5$

The new vertices will be $A'(0.5x_1,0.5y_1)$, $B'(0.5x_2,0.5y_2)$, $C'(0.5x_3,0.5y_3)$.

Step4: Dilate each vertex of the triangle for $k=-\frac{1}{2}$

The new vertices will be $A'(-\frac{1}{2}x_1,-\frac{1}{2}y_1)$, $B'(-\frac{1}{2}x_2,-\frac{1}{2}y_2)$, $C'(-\frac{1}{2}x_3,-\frac{1}{2}y_3)$.

Since we don't have the exact coordinates of the vertices of the triangles in the figures, we can't give the exact new - coordinates. But the general method for dilation of a point $(x,y)$ with scale factor $k$ is to get the new point $(kx,ky)$.

Answer:

For $k = 2$, multiply the $x$ and $y$ - coordinates of each vertex of the triangle by 2. For $k = 0.5$, multiply the $x$ and $y$ - coordinates of each vertex of the triangle by 0.5. For $k=-\frac{1}{2}$, multiply the $x$ and $y$ - coordinates of each vertex of the triangle by $-\frac{1}{2}$.